If we assume this condition does not hold, the theoretical model predicts negative profits.
One of the main reasons to assume this condition (SCP) is that they can use the Sobolev compact embedding H 2 ∩ H 0 1 ↪ L q ( 1 ≤ q < p ∗ ).
One of the main reasons to assume this condition (SCP) is that they can use the Sobolev compact embedding W 0 1, p ↪ L q , 1 ≤ q < p ∗.
(3.5) is convergent (in the following, we always assume this condition holds), then we have (lim_{mrightarrowinfty, mh=1}R z)^{m}=lim_{mrightarrowinfty,mh=1}R hp)^{m}=mathrm{e}^{p}), where (R z)=1+zb^{T} I-zA)^{-1}e) is T} I-zAbility function.
One of the main reasons to assume this condition (SCP) is to use the Sobolev compact embedding (H^{2}(Omega) cap H_{0}^{1}(Omega)hookrightarrow L^{q}(Omega)) ((1leq q< p^)).
When we cannot assume this condition, we decompose the total sequences into some groups, by using the criterion of the 100%% branching resolution in MP consensus tree.
Yet, we assume this condition is of some significance for the phyllocaridan ground pattern because similar, antero-lateral sclerites are also found in a member of the next closest relatives Eumalacostraca, the Hoplocarida (see below).
Given that its staminate flowers have pistillodes (vestigial carpels) and carpellate flowers have staminodes (vestigial stamens), it is assumed this plesiomorphic condition reflects evolution from an ancestor with bisexual flowers.
Incentive for migration are directed from country 1 to country 2, if and only if ∣m 2 ⋆∣<∣m 1 ⋆∣, and in the remaining of the paper, we will assume that this condition holds.
In MALDI imaging, it cannot always be assumed that this condition is met.
